HTMT above 0.90: distinguish unity tests from threshold inference

An HTMT estimate of 0.92 with a confidence interval below 1 does not establish HTMT below 0.90. These are different statistical questions. Decide which question and threshold you will use before inspecting results rather than choosing the most favorable criterion afterward.

What HTMT assesses

HTMT, the heterotrait-monotrait ratio of correlations, assesses empirical distinctiveness between reflectively measured constructs. Henseler, Ringle and Sarstedt (2015) proposed it and showed that Fornell–Larcker and cross-loadings can miss discriminant validity problems in simulated settings. Their original paper distinguishes point-estimate criteria from bootstrap inference.

A high HTMT prompts investigation of construct distinctions and item content. It does not identify an item that must be deleted or replace theoretically specifying the measurement model.

Separate three decisions

• A point-estimate rule compares HTMT with a previously justified cutoff, such as 0.85 or 0.90. Henseler et al. (2015) discuss both conventions.
• A unity test asks whether evidence supports HTMT below 1. This is the inferential question in the original Henseler et al. (2015) procedure.
• Threshold inference asks whether HTMT is below a chosen cutoff, such as 0.85 or 0.90, after accounting for uncertainty. SmartPLS documentation instructs users to compare the bootstrap upper bound with 0.90, following Franke and Sarstedt (2019).

An interval entirely below 1 may include 0.90 or lie entirely above it. Evidence against unity is therefore not equivalent to evidence supporting a 0.90 criterion.

A hypothetical example

Suppose HTMT = 0.92 and an illustrative bootstrap interval is [0.89, 0.95]. These are constructed numbers, not results from a published study. The upper bound is below 1 but above 0.90. Under an upper-bound-below-0.90 criterion, the result does not support discriminant validity. A theoretical explanation matters, but it does not make 0.95 smaller than 0.90.

Conversely, an estimate of 0.88 may fall below 0.90 while its bootstrap upper bound exceeds 0.90. Report both the estimate and uncertainty. A favorable point estimate does not make bootstrap evidence irrelevant.

A SmartPLS workflow

1. Check the measurement specification, construct definitions, reverse coding and overlapping item content. Do not apply HTMT indiscriminately to every pair of formative constructs.
2. Document the threshold and methodological justification in advance. Apply the same rationale to comparable pairs instead of switching from 0.85 to 0.90 to obtain a pass.
3. Select Calculate → Bootstrapping. SmartPLS recommends Complete (slower) and One-tailed for HTMT inference. Check the confidence interval method in your software version.
4. Under Quality Criteria, inspect original HTMT and the bias-corrected upper bound specified in the SmartPLS guidance. Compare with your chosen threshold. Record the resamples, significance level, test direction and interval method.
5. If evidence is insufficient, revisit theory, scale content, data quality and study design. Explain and report all measurement changes. Merging constructs solely to improve the table is not a sufficient justification.

A one-sided test at 5% and a two-sided 95% interval are not automatically equivalent settings. Record what was actually used. The original paper also addresses testing multiple construct pairs. Do not label every HTMT interval “95% CI” without checking.

Reporting the result

Hypothetical report: HTMT between A and B was 0.92. Its bootstrap upper bound was 0.95, exceeding the prespecified 0.90 cutoff. The result therefore did not support discriminant validity under the selected inferential criterion, although the illustrative interval was below 1. We further examined conceptual distinctions and item content.

Favorable Fornell–Larcker or cross-loading results do not automatically overturn a problem detected by HTMT. Present the evidence and model limitations, including unresolved uncertainty.

References

Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science, 43, 115–135. DOI 10.1007/s11747-014-0403-8.

Franke, G. R., & Sarstedt, M. (2019). Heuristics versus statistics in discriminant validity testing: A comparison of four procedures. Internet Research, 29(3), 430–447. DOI 10.1108/IntR-12-2017-0515.

SmartPLS. (n.d.). Discriminant validity assessment and HTMT.